A pole-vaulter approaches the takeoff point at a speed of 9.50 m/s. Assuming that only this speed determines the height to which he can rise, find the maximum height at which the vaulter can clear the bar.
KE= change in GPE= mgh
1/2 mv^2=mgh solve for h.
To find the maximum height at which the vaulter can clear the bar, we need to consider the conservation of energy.
The initial kinetic energy of the pole vaulter can be expressed as:
KE_initial = (1/2) * m * v^2
where m is the mass of the vaulter and v is the velocity.
As the vaulter reaches the maximum height, all of their initial kinetic energy will convert to potential energy. The potential energy can be calculated using the formula:
PE = m * g * h
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the maximum height.
According to the principle of conservation of energy, the initial kinetic energy is equal to the potential energy at the maximum height:
KE_initial = PE
(1/2) * m * v^2 = m * g * h
Canceling out mass (m) from both sides:
(1/2) * v^2 = g * h
Rearranging the equation to solve for h:
h = (1/2) * v^2 / g
Now, we can substitute the given values:
v = 9.50 m/s
g = 9.8 m/s^2
h = (1/2) * (9.50 m/s)^2 / 9.8 m/s^2
h ≈ 4.536 meters
Therefore, the maximum height at which the vaulter can clear the bar is approximately 4.536 meters.
To find the maximum height at which the pole-vaulter can clear the bar, we can use the principles of conservation of energy. The energy at the takeoff point will convert into gravitational potential energy at the maximum height.
First, let's identify the given information:
Initial speed (v) = 9.50 m/s
Gravity (g) = 9.8 m/s² (assuming Earth's gravity)
To find the maximum height (h), we need to calculate the potential energy (PE) at the highest point of the jump. Potential energy can be calculated using the formula:
PE = m * g * h,
where m is the mass and g is the acceleration due to gravity.
In this case, the mass of the pole-vaulter is not given, and we don't need it to find the maximum height since it cancels out in the energy equations.
We can equate the initial kinetic energy (KE) to the potential energy (PE) at the highest point:
KE = PE,
where KE can be calculated using the formula:
KE = 0.5 * m * v².
Substituting the values into the equation:
0.5 * m * v² = m * g * h.
Cancel out the mass (m):
0.5 * v² = g * h.
Now, rearrange the equation to solve for h:
h = (0.5 * v²) / g.
Substituting the values:
h = (0.5 * 9.50²) / 9.8.
Calculating:
h = (0.5 * 90.25) / 9.8,
h = 45.125 / 9.8,
h ≈ 4.60 meters.
Therefore, the maximum height at which the pole-vaulter can clear the bar is approximately 4.60 meters.